## MAS153 Mathematics (Materials)

Both semesters, 2019/20 | 20 Credits | ||||

Lecturer: | Prof Elizabeth Winstanley | Home page (also MOLE) | Timetable | Reading List | |

Aims | Outcomes | Teaching Methods | Assessment | Full Syllabus |

There are no prerequisites for this module.

The following modules have this module as a prerequisite:

MAS250 | Mathematics II (Materials) |

## Outline syllabus

- Permutations and combinations
- Binomial theorem
- Vectors
- Hyperbolic functions
- Differentiation
- Integration
- Series
- Complex numbers
- Matrices

## Aims

- To give students the necessary mathematical skills required to understand the scientific and engineering concepts introduced in the second year of their Material Science course.

## Learning outcomes

- Be able to calculate permutations and combinations
- Be able to apply the binomial theorem to series expansions and limits
- Understand vector algebra and be able to apply it to simple geometrical problems and to resolving forces
- Be able to manipulate hyperbolic functions and their inverses, and to carry out differentiation and integration involving hyperbolic functions and their inverses
- Be able to integrate using partial fractions, and to apply Simpson's rule
- Be able to verify solutions of simple ordinary differential equations
- Understand the concept of convergence of infinite series, and be able to test it using the alternating series test and the ratio test
- Understand and be able to use complex algebra
- Understand matrix algebra and be able to apply it to the solution of systems of linear equations, and to be able to find matrix eigenvalues and eigenvectors

## Teaching methods

Lectures, tutorials, independent study

40 lectures, 20 tutorials

## Assessment

One three-hour written examination for 80% of assessment.

## Full syllabus

**Permutations and combinations**

**The Binomial Theorem**

Pascal's Triangle, binomial theorem for positive integer exponents, extension to arbitrary real exponents, application to limits.

**Vectors**

Definition, magnitude, elementary algebra, component form, unit vectors, scalar product, angle between vectors, application to resolving forces, equations of lines and planes, vector product, scalar and vector triple products, a simple application to circular motion and angular momentum.

**Hyperbolic functions**

Definition in terms of exponentials, identities, inverse hyperbolic functions.

**Differentiation**

Inverse functions, hyperbolic functions and their inverses. Applications including Newton's 2nd law of motion, simple harmonic motion, radioactive decay, energy states of a particle in a 1D box.

**Integration**

Hyperbolic functions, use of hyperbolic functions in integration by substitution, use of partial fractions, Simpson's rule.

**Series**

Convergence, alternating series test, ratio test, Maclaurin and Taylor series.

**Complex Numbers**

Definition, conjugate, algebra. Argand diagram, modulus and argument, polar form. The Euler relation, De Moivre's theorem, roots of complex numbers, simple loci.

**Matrices**

Definitions (including diagonal and identity matrices), algebra, determinants, inverse matrices, homogeneous and non-homogeneous systems of linear equations, Gaussian elimination, eigenvalues and eigenvectors.

## Reading list

Type | Author(s) | Title | Library | Blackwells | Amazon |
---|---|---|---|---|---|

B |
Lambourne, R., Tinker, M. | Basic Mathematics for the Physical Sciences | Blackwells | Amazon | |

B |
Stroud, K.A., | Engineering Mathematics | Blackwells | Amazon |

(

**A**= essential,

**B**= recommended,

**C**= background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.

## Timetable (semester 2)

Mon | 17:00 - 17:50 | tutorial | (group MT1) | Hicks Lecture Theatre A | |||

Mon | 17:00 - 17:50 | tutorial | (group MT2) | Hicks Lecture Theatre E | |||

Thu | 12:00 - 12:50 | lab session | (group mt1) | Hicks Lecture Theatre 4 | |||

Thu | 12:00 - 12:50 | lab session | (group mt2) | Arts Tower Lecture Theatre 8 | |||

Thu | 13:00 - 13:50 | lecture | Arts Tower Lecture Theatre 4 |